What is the religious ruling on a father remarrying after the death of his wife, if his children object? And is the father allowed to disown them?

You have the right to marry, and your children are not permitted to prevent you from doing so. Rather, you should proceed with it if you are in need of it. As for your boycotting your children because of this, it is not permissible, because it involves severing ties of kinship, unless boycotting becomes the only way to reform them or to avoid their harm.